Boundary-Induced Apparent Risk Aversion in Nonergodic Multiplicative Growth

2026-07-30

AI Summary

This study addresses the misalignment between unbounded Kelly criterion assumptions and finite multiplicative growth systems terminated prematurely by absorbing boundaries, which can lead to misjudgments of risk preference. Focusing on finite-horizon binary multiplicative processes with an absorbing boundary, the authors fix ex ante risk exposure and terminal path residuals, employing an exact lattice propagation method to derive optimal strategies. They demonstrate that the geometric structure of the absorbing boundary naturally induces state-dependent, risk-averse-like behavior—even local super-Kelly reversals—without invoking heterogeneous risk preferences. Specifically, optimal exposure falls below the Kelly fraction near the boundary, yet may locally exceed it as the residual value approaches the boundary, thereby offering a structural explanation for apparent risk aversion.

Abstract

Finite multiplicative systems often cease to evolve when a lower continuation threshold is reached,whereas standard growth-optimal benchmarks assume uninterrupted continuation. We study a finite-horizon binary multiplicative process in which a fixed exposure is chosen ex ante and paths crossing an absorbing boundary are assigned a residual value. Exact lattice propagation yields the optimal exposure as a function of initial log distance to the boundary, horizon, and residual ratio. Costly absorption compresses exposure below the no-boundary Kelly fraction near the boundary. When interpreted through an unconstrained constant-relative-risk-aversion benchmark,this compression appears as elevated risk aversion. As the residual value approaches the boundary, a local above-Kelly reversal can occur. Absorbing-boundary geometry can therefore generate state-dependent risk-averse-looking behavior without heterogeneous primitive preference parameters.

Problem

• absorbing boundary
• multiplicative growth
• risk aversion
• Kelly criterion
• nonergodicity

Innovation

• absorbing boundary
• nonergodic growth
• Kelly criterion
• apparent risk aversion
• multiplicative processes